He previously found that the Insight journalists had defamed Cruddas with "cash for access" allegations and suggestions that he was prepared to accept foreign donations to the Conservative Party. The judge had also said they were liable for malicious falsehood, having had "a dominant intention to injure Mr Cruddas".

The decision follows Lady Justice Sharp's refusal in November last year to allow permission to appeal following an application on the papers.

Mr Cruddas sued over three of five stories which appeared in the newspaper on March 25, 2012.

The first, on the front page and then page 2, was headlined "Tory treasurer charges £250,000 to meet PM", and had a sub-heading saying "Cameron's fundraiser forced to resign".

The issue of the meaning of the articles was dealt with at a preliminary hearing and then went to the Court of Appeal.

It held that the first meaning was that in return for cash donations to the Conservative Party, Mr Cruddas corruptly offered for sale the opportunity to influence government policy and gain unfair advantage through secret meetings with the Prime Minister and other senior ministers, but that the stories had not alleged that Mr Cruddas had acted criminally, but that what he had said was "inappropriate, unacceptable and wrong and gave rise to an impression of impropriety".

The second meaning, it said, was that Mr Cruddas made the offer even though he knew that the money offered for secret meetings was to come, in breach of the ban under UK electoral law, from Middle Eastern investors in a Liechtenstein fund, and that to circumvent the law, Mr Cruddas was happy that the foreign donors should use deceptive devices, such as creating an artificial UK company to donate the money or using UK employees as conduits, so that the true source of the donation would be concealed.

Lord Justice Laws, who described the case as "unusual and in some ways troubling", said Richard Rampton QC, for the journalists, had argued that Mr Cruddas was prepared to contemplate receipt of donations in return for the prospect of commercial advantage in return for the prospect of commercial advantage through secret meetings with politicians at the top of government, and that that was "inappropriate, unacceptable, and wrong".

Lord Justice Laws – with whom Lord Justice Maurice Kay agreed – went on: "In order to obtain permission to make this case, Mr Rampton has to show a better than fanciful prospect of persuading this court that the judge went wrong on the facts to a radical degree.

"That is a tall order on any view, and it is right to note that the trial judge in this case has a wealth of experience in the field of defamation."

But there were "some singular features" in the case.

First, it was clear that the journalists, posing as representatives of foreign financiers, made it very plain that their interest in approaching the respondent was entirely commercial, Lord Justice Laws said.

He had concluded, though "not without misgiving" that Mr Rampton's points on the facts were enough to justify permission to appeal in relation to the cash for access allegation, he said, adding that he had "an uneasy sense" that Mr Justice Tugendhat might not, "despite his painstaking treatment of the case", have confronted the realities of the exchanges between the journalists and Mr Cruddas.

There was also force in Mr Rampton's argument that if he gained a fair wind on the cash for access issue, that might affect the court's approach to Mr Cruddas's attitude to the means of getting cash into this country from foreign donors.

On the malicious falsehood issue, Lord Justice Laws said it could not be fanciful to suppose that if Mr Rampton's case was good on cash for access, that might have an important influence upon the judgment to be made, on the facts, as to the charge of malice.

The finding of actual malice against the applicants was a serious matter, and he would give permission to appeal.

A spokesman for the newspaper said: "The Sunday Times is pleased that the Court of Appeal has given leave to appeal on this public interest case.

"The report, by our award winning investigations team, raised important issues of political significance so we are glad to have the opportunity to continue our legal challenge to the decision of Mr Justice Tugendhat."